Real-time evolution of a non-equilibrium non-Abelian plasma

Abstract

Real-time physical quantities of non-equilibrium processes in a non-Abelian plasma can be calculated either from extrapolating down from infinite high temperature $T$ and small coupling to intermediate couplings or by the means of the AdS/CFT correspondence which gives insight on strongly coupled gauge theories by the use of colliding shockwaves in Anti-de-Sitter (AdS) space. In this thesis we carry out anisotropic \emph{Hard Expanding Loop (HEL)} simulations in an expanding 1+1-dimensional and on full 3+1-dimensio\-nal plasma. We successfully reproduce semi-analytical results of the Boltzmann-Vlasov transport equation. The chromo-Weibel instability develops a strong growth of the soft fields both in the simpler abelian and in the non-abelian setup. We present results based on new initial conditions seeding unstable modes by currents fluctuations resulting in smaller onset times. The spectral analysis shows a characteristic energy flow from the low-frequency modes to higher frequency modes. We also study the numerical evolution of a supersymmetric Yang-Mills plasma created by the collision of gravitational shock-waves describing the horizon formation and energy evolution. We solve the initial value problem by evolving Einstein's equations numerically on a time dependent $\mathrm{AdS}_5$ background in this far-from-equilibrium situation.